GATE BT 2025 • Q46
MCQ • 2 Marks
Section 2: General Biotechnology
Biochemistry, Microbiology & Molecular Biology
Subtopic: Enzyme Kinetics, Cell Biology & Metabolism
Question Statement:
If the function
f(x) = {sin 2x , for x > 0,
a + bx, for x ≤ 0,
where a and b are constants, is differentiable at x = 0, then a + b is equal to
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2025 Q.46)**
**1. Governing Concept & Domain**:
This question evaluates **Biochemistry, Microbiology & Molecular Biology** under *Section 2: General Biotechnology* (2 Marks, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Biochemistry, Microbiology & Molecular Biology.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test